A circle has a sector with area $56\pi$ and central angle $315^\circ$. What is the area of the circle? ${64\pi}$ $\color{#9D38BD}{315^\circ}$ ${56\pi}$
Explanation: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{315^\circ}{360^\circ} = 56\pi \div A_c$ $\dfrac{7}{8} = 56\pi \div A_c$ $A_c \times \dfrac{7}{8} = 56\pi$ $A_c = 56\pi \times \dfrac{8}{7}$ $A_c = 64\pi$